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Simplifying 2w2 + 11w + 23 + -2w + 10w + 25 = 0 Reorder the terms: 23 + 25 + 11w + -2w + 10w + 2w2 = 0 Combine like terms: 23 + 25 = 48 48 + 11w + -2w + 10w + 2w2 = 0 Combine like terms: 11w + -2w = 9w 48 + 9w + 10w + 2w2 = 0 Combine like terms: 9w + 10w = 19w 48 + 19w + 2w2 = 0 Solving 48 + 19w + 2w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 24 + 9.5w + w2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + 9.5w + -24 + w2 = 0 + -24 Reorder the terms: 24 + -24 + 9.5w + w2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 9.5w + w2 = 0 + -24 9.5w + w2 = 0 + -24 Combine like terms: 0 + -24 = -24 9.5w + w2 = -24 The w term is 9.5w. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5w + 22.5625 + w2 = -24 + 22.5625 Reorder the terms: 22.5625 + 9.5w + w2 = -24 + 22.5625 Combine like terms: -24 + 22.5625 = -1.4375 22.5625 + 9.5w + w2 = -1.4375 Factor a perfect square on the left side: (w + 4.75)(w + 4.75) = -1.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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